One of the creatures glimpsed jumping out of the lift is one of the small monsters which attack people in the subway in "Cloverfield". The director of this movie, Drew Goddard, wrote Cloverfield.
The movie pays tribute to many famous horror movie monsters. The creature with the Buzz-Saws in its head with the Puzzle Orb is based off PinHead. Once it's free, you can see a Chatterbox-influenced cenobyte standing next to it. The people with ceramic masks who tie up and torture the scientists are based off The Strangers. The psychotic clown with the knife can either be seen as a tribute to PennyWise or Killer Clowns from Other Space. The massive killer bat is obviously from the movie BATS. A chainsaw can be heard as the different monitors are showing the slaughter - indicating LeatherFace. The ghoul-doctors operating on a victim while staring into the camera is based off House on Haunted Hill. The Red-Neck zombies brought to life through an incantation from a book is a tribute from The Evil Dead. The Scare-Crow-like zombies who kill the black security guard are based off of the movie ScareCrow.